METEO 300
Fundamentals of Atmospheric Science

3.2 Condensation and Evaporation

What is vapor pressure? Because of the Ideal Gas Law, we can think of vapor pressure (units = hPa or Pa) as being related to the concentration of water vapor molecules (or number of moles) in the atmosphere,

e= n v kTande=nR*T This equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers.

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where nv is the concentration of water vapor molecules (# cm-3), k is the Boltzmann constant (which is related to gas constant by R* = NAk, where NA is Avagadro's number of molecules per mole), and n is the number of moles per unit volume (n=N/V).

What makes liquid water different from ice or water vapor? It is actually the weak bonds between water molecules that are called hydrogen bonds. These bonds are 20 times weaker than chemical bonds and can be broken by collisions with other molecules if they are traveling fast enough and have enough kinetic energy to break the bonds. So the differences between vapor, liquid, and ice are related to the number of hydrogen bonds. In vapor, there are essentially no hydrogen bonds between molecules. In ice, each water molecule is hydrogen bonded to four other water molecules. And in liquid, only some of those hydrogen bonds are made and they are constantly changing as the water molecules and clusters of water molecules bump into and slide past each other.

spider web with drops of condensation
Water vapor condensed into liquid drops on a spider web overnight. As the sun rises and the air heats up, there will be net evaporation and the beads will shrink and disappear during the day.
Credit: devra via flickr

Look at a liquid water surface on a molecular scale. What is happening all the time is that some water molecules in the gas phase are hitting the surface and sticking (i.e., making hydrogen bonds), while at the same time other water molecules are breaking free from the hydrogen bonds that tie them to other molecules in the liquid and are becoming water vapor. The water vapor surface is like a Starbucks, but even busier. We can easily calculate the flux of molecules that are hitting the surface using simple physical principles, although it is harder to calculate the number that are leaving the liquid. Both are happening all the time, although usually the amount of condensation and evaporation aren't the same, so that we usually have net evaporation or net condensation.

In equilibrium, the flux of molecules leaving the surface exactly balances the flux of molecules that are hitting the surface. This condition is called equilibrium, or saturation. We can show that:

condensation evaporation = e e s = relativehumidity 100 This equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers.

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Thus, when RH = 100%, e = es, and w = ws. Condensation and evaporation are in balance. These two processes are going on all the time, but sometimes there can be more evaporation than condensation, or more condensation than evaporation, or evaporation equaling condensation. However, water is always trying to come into equilibrium.

So we know that the amount of water in vapor phase determines the condensation rate and thus e. So what determines es? We will see next that es depends on only one variable: temperature!